Exploring Radioactive Decay An Interactive Visual Learning Object

Exploring Radioactive Decay in Excel: An Interactive Visual Thinking Tool
Scott A. Sinex
Prince George’s Community College
Abstract
An interactive Excel spreadsheet investigation of radioactive decay kinetics and
associated measurement error is presented for use in general chemistry. Students
are engaged in numerous higher-order thinking and science process skills as they
work through the activity.
Keywords
Excel spreadsheet
discovery learning
radioactive decay kinetics
random and systematic error
Introduction
Radioactive decay is a general chemistry topic, usually covered late in the second
semester, and a typical example used to illustrate exponential behavior in
mathematics textbooks. Developing an interactive discovery-based activity for
examining aspects of radioactive decay was accomplished using the graphical and
numerical data display capabilities of Excel. The basics of developing interactive
computational Excel spreadsheets including an Excel tutorial are discussed in Sinex
(2004). Further Excel application support is also provided as links later in this
article (Sinex, 2005a). Discovery learning is in line with national reform efforts
(Siebert and McIntosh, 2001).
The tool consists of a series of questions that allow students to discover a number
of aspects of radioactive decay while examining an interactive multi-layered Excel
spreadsheet. There are five learning objectives to be addressed: (1) introduce the
basics of radioactive decay kinetics including determining half-life; (2) examine the
growth of the stable daughter nuclide produced from the parent nuclide; (3)
examine the behavior of an unstable or radioactive daughter nuclide (behavior of
consecutive reactions) including total radioactivity; (4) investigate the counting
error of the parent activity, its effects and correction, and; (5) investigate
background radiation and its effect and correction on the measurement. Numerous
higher-order thinking questions are posed throughout the activity along with the
Using Computers in Chemical Education Newsletter, Fall 2005 1
Using Computers in Chemical Education Newsletter, Fall 2005 1
application of science process skills. The interactive dynamic nature of the
technology employed enhances the discovery learning of both chemical and
mathematical concepts in freshman chemistry for non-majors. Recently, Lim
(2003) has outlined some advantages of using spreadsheets in chemistry, where in
quantum chemistry the symbolic mathematics is purposely hidden due to its more
complicated nature.
This activity is done having covered chemical kinetics earlier in the semester and
with an introduction to radioactive decay via the penny or M&M flipping activity to
uncover the exponential nature of decay and define half-life. The statistical
nature of the process is discovered and the appropriate mathematical relationships
can be derived. Students have used Excel as a data handling, graphing, and
analyzing tool in their general chemistry experience and we provide support
documentation (Sinex and Gage, 2001). Experience with Excel is not really
necessary to use this spreadsheet; although students should be introduced to using
an interactive spreadsheet. A large percentage of our students come into general
chemistry with Excel experience; however, it generally does not involve plotting
scientific data.
Here are the links to the files:
student activity interactive spreadsheet
Interactive Excel Spreadsheet
The approach of questioning drives the student to discover concepts as they
explore the interactive spreadsheet. Students are going to perform numerical
experiments and address many “what if” scenarios; hence, they are engaging in
science process while learning. The questions are keyed to the tabs (lower left of
screen) on the Excel spreadsheet as shown below in Figure 1.
Figure 1 – Tabs of multilayered Excel Workbook
Using Computers in Chemical Education Newsletter, Fall 2005 2
Using Computers in Chemical Education Newsletter, Fall 2005 2
A number of adjustable variables, where values are typed in (shown as yellow cells)
or adjusted with sliders (scroll bars as referred to in Excel on the Forms toolbar),
are included on each worksheet. As they are adjusted, the graphs and data in
columns respond and regressions are re-evaluated as well. Comment cells, indicated
by a small red triangle in the upper right corner of the cell, are included to offer
explanation. A number of these features are illustrated on the screen shot (Figure
2) from the counting error tab worksheet given below.
Figure 2 – Screen shot of Counting Error Tab
For novices to these interactive spreadsheets or simulations, it is generally
recommended to adjust the variables in a systematic way (low to medium to high or
vice versa) and to explore the full range of the variable. Excel’s data validation
feature is used in some cases to set specific limits on variables. Conditional
formatting is used to enhance patterns (cell background color changes) in numerical
data such as the random error and safe worksheets. Each worksheet has the
Protect Sheet… selected under the Tools to prevent students from accidentally
modifying formulas. This can be turned off by selecting Unprotect Sheet… to
allow modification or generation of other plots. Password protection and the
ability to hide formulas are also available options.
Using Computers in Chemical Education Newsletter, Fall 2005 3
Using Computers in Chemical Education Newsletter, Fall 2005 3
The unstable daughter situation allows the introduction of consecutive reactions (A
B C). From the graphical display students can discover that the slower step
(longer half-live) controls the overall rate. Use of the total radioactivity or the
sum of the parent plus radioactive daughter makes this easy to follow as
illustrated in Figure 3.
Figure 3 – Unstable Daughter Plots
The investigation of counting error and background uses adjustable random noise
added to the data via the RANDBETWEEN function available in the Analysis
ToolPak of Excel (loading instructions included on spreadsheet, see the last tab).
The equation given below illustrates how adding error to the activity, Ameasured, was
accomplished:
Ameasured = Atheoretica l + x[RANDBETWEE N( −10,10) ]
The RANDBETWEEN function is set to generate random numbers between -10 to
10 in this case. The “x” variable is then tied to an adjustable slider that can be
adjusted from zero to some upper limit. Atheoretical is simply based on exponential
decay, Aoe-kt. Hence, the noise can be removed (set x = 0) or increased to examine
Using Computers in Chemical Education Newsletter, Fall 2005 4
Using Computers in Chemical Education Newsletter, Fall 2005 4
its consequence. If your students are not used to dealing with scatter and its
effects in data analysis, see Sinex (2005b). The %Error graph in Figure 2 shows
how relative error grows larger at later times. Students can discover that
increasing initial activity, Ao, can reduce the random counting error.
Student Feedback and Assessment
A survey of 23 students that used this activity in spring 2005 showed that 74%
had no difficulty in usage and 65% thought it helped them understand the
concepts, due to its interactive and/or visual nature. The graphs were indicated as
the most common (43%) valuable aspect. The background and counting errors
proved to be the most difficult (35%) as this was totally new material not
discussed in class. One student commented “I learned through my own actions and
got to manipulate my own data. I felt more like an active learner,” while another
suggested to “do without the Excel.” When the students were asked to have the
option of the interactive activity or lecture, 57% wanted their instructor to just
lecture. However, research such as Oliver-Hoyo and others (2004) has shown
otherwise.
Assessment is accomplished by having students analyze a set of data (which can be
easily modified from semester-to-semester or even student-to-student) to
evaluate the half-life of a radioactive isotope and examine experimental error.
Figure 4 illustrates the scoring (out of 25 points) for the assessment, labeled as
project, and a follow-up set of similar questions with different data on the final
Figure 4 – Assessment Scores Comparison
Using Computers in Chemical Education Newsletter, Fall 2005 5
Using Computers in Chemical Education Newsletter, Fall 2005 5
exam. The project is an out-of-class assignment and may be worked on in groups
with each student submitting results. Of the 24 students that completed both,
42% showed an increase or achieved maximum points, while 17% (four large
negative differences) showed that learning should be stressed in cooperative
learning activities.
Discussion
As students work through this learner-centered activity, discussion of chemical
concepts is included at a number of points and the connections to the mathematics
are emphasized as well. We deal with the daughter nuclide and the “conservation
of nuclides” to remind students of the product in the decay reaction. The unstable
daughter is an introduction to consecutive reactions and useful for discussion of
decay series, such as 238U, or radioactive generators in nuclear medicine. The
discussion also distinguishes between random and systematic errors. Error is
introduced earlier as part of the laboratory to this course; see Sinex (2005c) for
further discussion. Counting error is random in nature. This random variation in
the counts becomes a serious problem when the total counts are small numbers at
later times. Larger percent errors can greatly influence the exponential
regression results. Background radiation induces a systematic error, which has the
largest effect at low activities and has a major influence on the resulting
exponential regression if left uncorrected. They also research information on
background radiation with proper citation of their sources. An instructor can
generate a new set of data for assessment using the background tab worksheet
and adjusting the half-life, starting activity, counting error, and background level.
Data generated by the instructor can be copied from Excel and pasted into a Word
document as a table for students to analyze.
The advantages of the interactive Excel spreadsheet in general chemistry are
numerous and include the following:
● readily available off-the-shelf software;
● students have previous experience with Excel;
● disguises the mathematical computations to allow easier integration of the
mathematical aspects with less anxiety;
● provides visual display of graphs with multiple variables plotted along with
numerical data and symbolic relationships;
● emphasizes data modeling with analysis and interpolation;
● strengthens the connection between science and mathematics;
Using Computers in Chemical Education Newsletter, Fall 2005 6
Using Computers in Chemical Education Newsletter, Fall 2005 6
● interactivity allows comparison and exploration of variables (a poor man’s
simulation package) through numerical experimentation;
● easily modified, and;
● enhances discovery-based learning through “what if” scenarios.
Other topics explored by students in Excel include a review of mathematical
functions for modeling, investigating the gaseous state of matter, velocity
distribution for gases, acid distribution diagrams (monoprotic, diprotic, and
triprotic acids), chemical kinetics, consecutive and competing reactions, and Beer’s
Law (Beer’s Law activity).
Students are exposed to the topic of radioactive decay via a hands-on minds-on
investigation using available technology that enhances the graphical and numerical
nature of the kinetic behavior. The nature of radioactive decay and its
measurement error are explored through a mathematical modeling approach, which
is in itself good science process. With the proper mode of questioning, a little
simulation can generate a wealth of reasoning by students. The dynamic nature of
interactive spreadsheet brings the mathematics “alive” for students, as novice
learners do not readily see this in mathematical equations. This approach works to
strengthen the “rule of four,” through which mathematics educators (AMATYC,
2005; NCTM, 2000) are trying to emphasize and relate graphical, numerical,
symbolic, and verbal descriptions. In the end, the technology helps students
develop an understanding of concepts involving radioactive decay (Sherman and
Kurshan, 2004).
References
AMATYC (2005) Beyond Crossroads: Implementing Mathematics Standards in the
First Two Years of College. American Mathematical Association of Two Year
Colleges (online).
<http://http://amatyc.org/Crossroads/CROSSROADS> Accessed 17 November
2005.
Lim, K. (2003) Using Spreadsheets in Chemical Education to Avoid Symbolic
Mathematics, Using Computers in Chemical Education Newsletter, Spring 2003.
Accessed 17 November 2005.
NCTM (2000). Principles and Standards for School Mathematics. National Council
of Teachers of Mathematics (NCTM), Reston, VA.
Using Computers in Chemical Education Newsletter, Fall 2005 7
Using Computers in Chemical Education Newsletter, Fall 2005 7
Oliver-Hoyo, M.T., Allen, D., Hunt, W.F., Hutson, J., and Pitts, A. (2004) Effects of
an Active Learning Environment: Teaching Innovations at a Research I Institution,
Journal of Chemical Education 81 (3): 441-448.
Sherman, T., and Kurshan, B. (2004). Teaching for Understanding. Learning and
Leading with Technology 32 (4): 6-11.
Siebert, E.D. and McIntosh, W.J. (2001) College Pathways to the Science
Education Standards, National Science Teachers Association (NSTA) Press,
Arlington, VA.
Sinex, S.A. (2004) An Interactive Higher-Order Thinking Tool, TechLearning
Educator's Outlook. Accessed 17 November 2005.
Sinex, S.A. (2005a) Developer's Guide to Excelets: Dynamic and Interactive
Visualization with "Javaless" Applets or Interactive Excel Spreadsheets. Accessed
17 November 2005.
Sinex, S.A. (2005b) Exploring the Goodness of Fit in Linear Models, Journal of
Online Mathematics and Its Applications 5. Accessed 17 November 2005.
Sinex, S.A. (2005) Investigating Types of Errors, Spreadsheets in Education 2 (1)
115-124. Accessed 17 November 2005.
Sinex, S.A. and Gage, B.A. (2001) Using Excel for Handling, Graphing, and Analyzing
Scientific Data: A Resource for Science and Mathematics Students. Accessed 17
November 2005.
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Using Computers in Chemical Education Newsletter, Fall 2005 8